An Algorithm for Estimating Reachable Set of Control System under Uncertainties

The paper deals with the problem of external ellipsoidal estimation of the reachable set of the bilinear control system with uncertainties in the system matrix and in the initial states. It is assumed that the unknown initial states of the system belong to a given symmetric star-shaped set of a special type. The matrix of linear terms in the phase velocities of the system is unknown. The dynamic of the system is complicated by the presence of bilinear components in the right-hand side of the system di fferential equation. In this study, a new class of uncertainties in the parameters of the system matrix is considered. Under such constraints, the dynamical system is nonlinear, and the reachable set loses the property of convexity. The Minkowski gauge functions are used for the description of star-shaped reachable sets. The main result is the algorithm that allows constructing external ellipsoidal estimates of the reachable set for the considered system based on the technique of set-valued estimation.